Predicting Values with Linear Mixed Modeling: A Comprehensive Guide to Overcoming Challenges of Nesting Effect

Linear Mixed Modeling with Nesting Effect: A Comprehensive Guide to Predicting Values

Introduction

Linear mixed modeling is a statistical technique used to analyze data that has multiple levels of nesting. In this article, we will delve into the world of linear mixed modeling and explore how to predict values using a model developed with this method. Specifically, we will focus on the nesting effect in the model and provide guidance on how to overcome common challenges when predicting values.

What is Linear Mixed Modeling?

Linear mixed modeling is an extension of traditional linear regression that allows for the inclusion of random effects, also known as variance components or covariates. These random effects capture the variation within groups or clusters, which can be particularly useful in fields like medicine, psychology, and sociology where data is often collected at multiple levels.

In the context of our example, we are using linear mixed modeling to develop a model that predicts Reduction.factor based on 5 predictor variables: PAI, Open.wind, Temp, Height, and Density. The (1|PAI:Open.wind) term in the model specification indicates that the intercept is nested within the group defined by PAI:Open.wind. This means that for each unique value of PAI:Open.wind, we have a separate set of coefficients.

Model Specification

The R code provided in the question shows how to specify the linear mixed model:

model1 <- lmer(Reduction.factor ~ (1|PAI:Open.wind) + 
     (1|PAI:Temp) + (1|PAI:Height)+ (1|PAI:Density)+ PAI  ,
    data = model)

In this specification, we have three levels of nesting:

PAI:Open.wind: This is the first level of nesting, which means that for each unique value of PAI:Open.wind, we have a separate set of coefficients.
PAI:Temp and PAI:Height: These are the second level of nesting, which means that for each unique combination of values in PAI:Open.wind and Temp/Height, we have another set of coefficients.
The final term PAI is the third level of nesting, which means that for each unique combination of values in the previous levels, we have a separate set of coefficients.

Data Preparation

To predict values using this model, we need to prepare our data. In the question, the author provides a dataframe case study with 8 rows and 5 columns: Temp, Height, Density, PAI, and Open.wind.

Temp    Height  Density PAI Open wind
20.000  0.041   0.033   1.960   30.000
20.000  0.082   0.061   1.960   30.000
20.000  0.122   0.059   1.960   30.000
20.000  0.163   0.061   1.960   30.000
20.000  0.204   0.043   1.960   30.000
20.000  0.245   0.048   1.960   30.000
20.000  0.286   0.052   1.960   30.000
40.000  0.082   0.061   1.960   40.000
40.000  0.122   0.059   1.960   40.000
40.000  0.163   0.061   1.960   40.000
40.000  0.204   0.043   1.960   40.000
40.000  0.245   0.048   1.960   40.000
40.000  0.286   0.052   1.960   40.000

Predicting Values

The author provides the following R code to predict values:

p1 <- predict(model1, case study)

However, this results in an error message “Error in (function (x, n) : new levels detected in newdata”.

To resolve this issue, we need to ensure that the predictor variables are at their correct level of nesting. In our example, PAI:Open.wind is the first level of nesting, so we should use this as the grouping variable when predicting values.

We can modify the R code to achieve this:

p1 <- predict(model1, case study, se = TRUE, interval = "confidence")

The additional arguments se = TRUE and interval = "confidence" specify that we want to calculate the standard errors and confidence intervals for our predictions.

Confidence Intervals

When predicting values with a linear mixed model, it’s essential to consider the uncertainty in our estimates. This is where confidence intervals come into play. By providing a range of plausible values, we can gain more insight into the variability of our predictions.

The interval = "confidence" argument specifies that we want to calculate 95% confidence intervals for our predictions. We can adjust this parameter to suit our specific needs.

Conclusion

In conclusion, predicting values with a linear mixed model requires careful consideration of the nesting effect in the model. By understanding how the predictor variables are at different levels of nesting, we can ensure that our predictions are accurate and reliable.

We also need to be mindful of the uncertainty associated with our estimates, which is where confidence intervals come into play. By providing a range of plausible values, we can gain more insight into the variability of our predictions and make more informed decisions.